Probability of a Straight Flush

Date: 5/15/96 at 14:44:22
From: Art Mabbott
Subject: Probability Problem

My high school math topics class is trying to work through a
probability problem involving counting and trees.  The question 
involves finding the probability of drawing 5 spades, that is 
P(a flush) = (13 12 11 10 9)/(52 51 50 49 48) P(flush of any suit) 
= 4 P(a flush)

The question is, what is the P(Straight flush) = ?  (knowing that
there are only 10 ways in each suit to draw a straight flush). 

Art Mabbott

Date: 5/17/96 at 19:0:51
From: Doctor Ken
Subject: Re: Probability Problem

Hello!

Something that will help in these problems is the "choose" formula.  
If you want to know the number of ways you can choose 5 cards from a 
deck of 52 cards, when the order of the cards doesn't matter, then the 
answer is 52 choose 5, which is 

 52!/(5!(52-5)!) = (52 51 50 49 48)/(5 4 3 2 1).  

So that's the total number of different hands you could be dealt.

Since you've already figured out how many different ways you can get a 
straight flush (actually, are you sure it's 10 in each suit?  I get 9, 
because A2345 doesn't count, right?), you can just divide the number 
of straight flushes by the number of possible hands to get the 
probability you're dealt a straight flush.

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/